Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-14" was replaced by "^(-14)". 1 more similar replacement(s)

(2): "2.5" was replaced by "(25/10)".

Step  1  :

 1.1     10 = 2•5

(10)^-14 = (2•5)^(-14) = (2)^(-14) • (5)^(-14)

Equation at the end of step  1  :

  )25
  ——— • ((2)(-14)•(5)(-14)))
  (10

Step  2  :

            5
 Simplify   —
            2

Equation at the end of step  2  :

  )5
  —— • ((2)(-14)•(5)(-14)))
  (2

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2¹⁴   = 2^{(1 + 14)} = 2¹⁵

Raising to a Power :

 3.2    5¹   divided by   5¹⁴   = 5^{(1 - 14)} = 5^(-13) = ¹/_5¹³

Equation at the end of step  3  :

  14))1 
  —————————
  (215•513) 

Step  4  :

 4.1     10 = 2•5

(10)^-14 = (2•5)^(-14) = (2)^(-14) • (5)^(-14)

Equation at the end of step  4  :

  4)))1 
  —————————
  (215•513) 

Step  5  :

             1              1    
 Divide  —————————  by  —————————
         (214•514)       (215•513) 

 5.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

    1             1               1         (215•513) 
—————————  ÷  —————————   =   —————————  •  —————————
(214•514)      (215•513)        (214•514)          1    

Dividing exponents :

 5.2    2¹⁵   divided by   2¹⁴   = 2^{(15 - 14)} = 2¹ = 2

Dividing exponents :

 5.3    5¹³   divided by   5¹⁴   = 5^{(13 - 14)} = 5^(-1) = ¹/_5¹ = ¹/₅

Final result :

  2           
  — = 0.40000 
  5